At risk of earning the hurling of rotten tomatoes at me...I actually have no problem with this series but one.
Basically, boiled down to it's essence, the constant critical history of prog rock's death in the 1970s was "people went to listen to punk because they were tired of how over the top ELP and Yes got." And despite being a prog head and loving both ELP and Yes to death...they have a point. ELP's hilarious stage shows and pretentious adaptations of classical pieces, Yes recording a double album with only four songs on it and doing rock concerts where you had to be seated before the show started, where the band promptly hit you with 82 minutes of new music at once-neither move was the sort of thing that you'd call audience friendly. These were progressive ROCK bands, and I can see, very clearly, where some rock fans could see bands doing this sort of thing and think "but I just want to ROCK." As much as I love 36 minute long versions of Karn Evil 9 and the bulk of Topographic Oceans (I still can't get into The Ancient, and I doubt I ever will), it's easy to see them from the outside as being breaking points where even prog fans said "okay, we're getting a little goofy here."
Where this series has a problem is that the first two parts are clearly written as love letters to Keith Emerson, and as such provide nowhere near enough context for the growth of prog. Part 3, which is supposed to come across as the part where ELP gets slammed, also reads like a fanboy appreciation. Without the proper context for the growth of prog, which really doesn't come until Part 4, it does feel like out of the blue, this series blames Yes and solely Yes.
A lot of things caused prog to "die". But one of them WAS the reaction that many people, including fans of the genre, had to Topographic Oceans. The problem comes when this is presented as the sole reason, rather than a symptom.